# Effective Noise Temperature

The temperature at which the resistor’s resistance equals the noise power produced by the circuit or device is known as the effective noise temperature. Use of the effective noise temperature is common in the telecommunications sector.

The source noise temperature in a two-port network or amplifier, which is connected to a noise-free network or amplifier, will produce the same output noise power as that of the actual network or amplifier linked to a noise-free source, such temperature obtained is known as the effective input noise temperature. The effective noise temperature can also be calculated using the formula

T_{n}= 290(F – 1)where,

Fis the numeric noise factor290 Kis the standard noise temperature.

## Effective Noise Temperature Formula

Effective Noise Temperature can be computed by using the formula,

T = N / kBwhere,

Nis amount of noise inside a given bandwidth.Bis the bandwidthKis the Boltzmann constant, which is approximately equal to 1.38 x 10^{-23}JK^{-1}

## Noise Figure

The signal-to-noise ratio at the input to that at the output is known as the noise figure for an electronic system. Determining how much the signal is decreased at the output due to noise is a useful parameter. The total noise power in the circuit, as well as the frequency range involved, affects a system’s noise temperature. The formula below can be used to calculate the relationship between the noise figure and noise temperature.

NF = 10 log_{10}[(T_{noise }/ T_{ref}) + 1]where,

NFis Noise figureTis Noise Temperature_{noise}Tis Reference temperature. Normally the Ambient temperature._{ref}

## Solved Problems on Effective Noise Temperature

**Problem 1: In a particular circuit, a resistor has a noise bandwidth of 20 Hz. Determine the effective noise Temperature. **

**Solution: **

Given :

Noise in the bandwidth (N) = 20 Hz

Effective Noise Temperature can be calculated by the formula,

T = N/kB

we known, K is the Boltzmann constant, which is approximately equal to 1.38 x 10

^{-23}JK^{-1}T = 20 / 1.38 x 10

^{-23}T = 4.799 x 10

^{-10}kelvin

**Problem 2: Consider a circuit with a resistor that has a noise bandwidth of 45 Hz. Determine the effective noise Temperature. **

**Solution:**

Given :

Noise in the bandwidth (N) = 45 Hz

Effective Noise Temperature can be calculated by the formula,

T = N/kB

we known, K is the Boltzmann constant, which is approximately equal to 1.38 x 10

^{-23}JK^{-1}T = 45 / 1.38 x 10

^{-23}T = 1.08 x 10

^{-9}kelvin

**Problem 3: Determine the Noise Figure, if the reference temperature and the noise temperature are given which are 290 kelvin and 35 kelvin respectively. **

**Solution: **

Given :

Reference Temperature (T

_{ref}) = 290 kelvinNoise Temperature (T

_{noise}) = 35 kelvinNoise Figure can be calculated by the formula,

NF = 10 log

_{10}[(T_{noise}/T_{ref}) + 1]NF = 10 log

_{10}[(35 / 290) + 1]NF = 0.4949 dB

Therefore, the value of Noise Figure is 0.4949 dB.

**Problem 4: The reference temperature and the noise temperature are given, which are 290 kelvin and 68 kelvin respectively. Calculate the Noise Figure for the above-given data.**

**Solution:**

Given :

Reference Temperature (T

_{ref}) = 290 kelvinNoise Temperature (T

_{noise}) = 68 kelvinNoise Figure can be calculated by the formula,

NF = 10 log10 [(Tnoise/Tref) + 1]

NF = 10 log10 [(68 / 290) + 1]

NF = 0.9149 dB

Therefore, the value of Noise Figure is 0.9149 dB.

## FAQs on Effective Noise Temperature

**Question 1: What is the Noise temperature of an Amplifier?**

**Answer: **

The noise temperature of an amplifier is the temperature of a resistance, if its input were terminated with a noise-free resistance, It would create the same amount of noise power at its output as the actual amplifier.

**Question 2: Explain the relationship between noise temperature and noise figure.**

**Answer: **

The noise figure number, which is measured in decibels (dB), tells how well an amplifier or RF receiver performs. The noise temperature is defined as the temperature required to generate an equivalent amount of Johnson-Nyquist Noise.

**Question 3: What is a good noise figure?**

**Answer: **

The ideal level is 0 dB, which denotes that the gadget generates exactly the same amount of noise as it receives. In this situation, we can state that our system has a decibel Noise Figure of 0.

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